On Saturday morning at 9am a convoy of 80 coaches will trundle away from Hull's KC Stadium going south to Wembley and on the M1 a thousand car wing mirrors will stream with amber flags. In 110 years of sweat and struggle since their club was formed in 1904, the supporters have never been able to say this before: Hull City are in the FA Cup final. Fans have been posting pictures of their tickets on the internet, ecstatic that they bear Hull City's name for a final against the football aristocracy of Arsenal.

At the end of a Premier League season in which the club's name has sparked a divisive tussle with the owner, Assem Allam, who planned to change it to Hull Tigers, they have all come together now, hoping their colours are on the cup.

Their manager Steve Bruce, having retained the club's Premier League status for next season, said this week that Hull's presence against Arsenal is a "classic" FA Cup contest, a reminder of the competition's "beauty" which has faded in the Premier League's shadow over recent years. Bruce, in tandem with his longest serving player, Liam Rosenior, talked earnestly this week about how much the final means to a tough, economically neglected city trying to resurrect its fortunes.

"Just five minutes from the stadium you will see there is not much money, there has been no investment in the area for a long time," said Rosenior, who was the Allam regime's first signing in October 2010. "The people here are proud, though, and to have a team representing them in the FA Cup final means the world to them. For me to be part of it is really special."

Ian Ashbee, the former captain who attained the extraordinary career achievement of playing for Hull City up through all four divisions between 2002 and 2011, said people are "ecstatic". He played at the old, creaking Boothferry Park ground, where "the fans were always very loyal; they turned up in big numbers", but "never would have dreamt that 12 years later they would get to an FA Cup final".

The supporters are struggling with their disbelief after all the club has been through: existence-threatening administration in 2001, the bottom division as recently as 2004, dicing with liquidation again after relegation from the Premier League in 2010. Bob Horton, who runs the official supporters club's Driffield branch – fondly nicknamed "heart attack Bob" after suffering two coronaries during Hull City matches – shattered his ankle last week but will be at Wembley for this once-in-a-lifetime event.

The romance of a northern city with the bunting out, decamping for the FA Cup final in London, is almost as old as the professional game itself. But Hull's long journey to Wembley has more dimensions than just a gleeful day out. There are the prices, which at the top rate have been too much for Hull fans – the club has sold its entire 25,000 allocation of tickets except for some of the £115 best seats. The return coach journey to Wembley is £31, which the club says it is doing at cost, but there have been complaints nonetheless from the many fans who have already forked out for tickets at £85 a time.

Hull's civic leaders have dug into their historic character and found a voice recently, unifying the old shipping and fishing hardiness, the heritage of the poet Philip Larkin and the anti-slavery campaigner William Wilberforce to land City of Culture status for 2017. Pauline Davis, the council's deputy chief executive, standing on Tuesday outside the Ferens Art Gallery, one of the cultural gems councillors show visitors when pressing their case, said: "There has always been a pride in Hull and now, with having a Premier League football team, at Wembley and in Europe next season, and being City of Culture, we are looking out again, creating hope in the future."

Davis acknowledges that Hull is "10 years behind" Manchester, Leeds and Liverpool in its recovery efforts in the wake of industrial decline but in a grand Victorian city square markedly less bustling than in those cities it seemed more like 20 at least. After Manchester became expert in the 1990s at bidding for whatever grants and lottery money were going for the battered provinces, it bagged a new arena, concert hall, conference centres, a tram system, and the 2002 Commonwealth Games, including its £127m stadium, which ultimately attracted Abu Dhabi money to Manchester City. Hull got nothing at all. The Deep, Hull's popular aquarium attraction, was a millennium project.

After fishing and its associated industries collapsed and the port, although still flourishing, became highly mechanised, Hull never found economic ballast. Public administration, education and health were marooned as the biggest employers. Since 2010 the government has cut £104m from the council's budget, with a further £48m going this year and next. Hull has the highest proportion of people on jobseekers allowance (6.6%) in the country, and 22% of people aged 16-64 are economically inactive. A decision by the German company, Siemens, to site a new wind turbine factory in the city has been welcome but government delays and funding reductions for windfarms mean the expected new jobs, 3,000 including at supply companies, are far fewer than the 10,000 originally planned for.

Hull City, like many Premier League clubs now, looms like a multimillion pound island of glitz, fenced off from its rundown surroundings, rather than a football flagship for the people. But Rosenior says he and his handsomely paid team-mates are aware of the realities around them. "There are misconceptions about footballers, that we're all womanisers, drinkers, gamblers," he said. "Most footballers are working class lads, who have to be honest and work hard to get to this level, and our team is like that. We see the poverty in this area, a lot of people on the breadline, and we hope we're helping to re-invigorate some pride. Most footballers are just normal guys that are living their dreams. I'm playing in an FA Cup final on Saturday and that is what I wanted to do from the age of five."

One reason Rosenior is living that dream is because, amid all the grim decline, the council found the money to give a great gift to the club – the KC Stadium. With no government or lottery cash available, the council spent £43.5m on building the stadium, using some of the proceeds from the sale of Kingston Communications, Hull's white telephone box company, in 1999. At the time the club was plunging into one of its darkest episodes under the stewardship of its part-owner Stephen Hinchliffe, who in February 2001 was sentenced to five years in prison (reduced to four on appeal) for bribery and corruption relating to his collapsed company, Facia. City had famously been locked out of Boothferry Park after missing rent payments to the ground's owner, the tennis entrepreneur David Lloyd, who had sold the stadium to Hinchliffe's consortium. The club fell into administration.

Adam Pearson, the former Leeds United commercial director, backed by a Leeds entrepreneur, Peter Wilkinson, bought the club, and the council then had sufficient confidence to furnish them with the stadium. Ashbee, signed by Jan Molby after six years at Cambridge United, recalls the move to the 25,586 all-seat stadium as "a real step change". Peter Taylor, who replaced Molby in October 2002, managed Hull teams to two promotions and into the Championship by 2006.

The 2008-10 stint in the Premier League under Phil Brown is best remembered for the 30-yard swerving strike that the Brazilian striker Geovanni scored in a 2-1 victory away at Arsenal, a memory that gives Hull fans hope for Wembley. City were relegated in 2010; the then owner, Russell Bartlett, had moved millions out of the club to finance his own company, and Allam says City were facing liquidation until he bought it and paid off a £17m tax bill.

That money helped to finance Bruce's key signings last summer: Tom Huddlestone and Jake Livermore from Tottenham Hotspur and Curtis Davies from Birmingham City. Allam backed Bruce to spend £13m in January on the strikers Nikica Jelavic, from Everton, and Shane Long, from West Bromwich Albion, whose goals helped Hull stay in the Premier League. But both are Cup-tied and have sat out the triumphant march to Wembley.

Allam, talking to the Guardian at his industrial generator factory last week, kept his pledge not to discuss his Hull Tigers name change plan, which he argues will be commercially advantageous, but which the FA has refused to sanction. "Everybody is excited, we have made history," he said. "After the end of the season then we talk about changing the name. That relates to the future."

Ian Waterson, a fan and spokesman for the City Till We Die campaign, which made a submission to the FA – arguing for the City name to be kept – is prepared to let sleeping dogs lie for the moment and is thrilled that the final has come around. "There is still magic in the FA Cup," he said. "We went through dark days years ago and we are grateful to the Allams. It is unbelievable that we are now in an FA Cup final."

If Bruce's team of assembled workers can beat Arsène Wenger's craftsmen at Wembley, if their name really is on the Cup, it will be engraved for always as Hull City, whatever happens next.